In this work we propose an algorithm for trace recovery from stochastically known logs, a setting that is becoming more common with the increasing number of sensors and predictive models that generate uncertain data. The suggested approach calculates the conformance between a process model and a stochastically known trace and recovers the best alignment within this stochastic trace as the true trace. The paper offers an analysis of the impact of various cost models on trace recovery accuracy and makes use of a product multi-graph to compare alternative trace recovery options. The average accuracy of our approach, evaluated using two publicly available datasets, is impressive, with an average recovery accuracy score of 90-97%, significantly improving a common heuristic that chooses the most likely value for each uncertain activity. We believe that the effectiveness of the proposed algorithm in recovering correct traces from stochastically known logs may be a powerful aid for developing credible decision-making tools in uncertain settings.